1. Field of the Invention
The present invention relates to a wideband signal analyzing apparatus, a wideband period jitter analyzing apparatus, and a wideband skew analyzing apparatus for analyzing an input signal. More particularly, the present invention relates to a wideband signal analyzing apparatus, etc. for analyzing a wideband input signal.
2. Description of the Related Art
The high speed serial input/output technology makes it possible to perform high speed data transmission at a data rate of 2.5 Gbps. Further, the transmission rate reaches 6.5 Gbps in the Year 2005. In the past five years, the timing jitter or the period jitter has been measured mainly using a time interval analyzer or a real time oscilloscope. Since it is necessary to estimate whether at least a pair of zero-crossings adjacent to each other are continuously sampled or not, the measurement limit of the time interval analyzer or the real time oscilloscope is about 4.5 Gbps or 2.5 to 3 Gbps respectively. In order to measure the jitter at 6.5 Gbps, it is necessary to significantly improve the performance of the hardware (particularly, an analog-to-digital converter or an extremely high speed counter). Meanwhile, an equivalent sampling oscilloscope sequentially shifts the timing of a sampling pulse at the time of a trigger, undersamples a waveform at such a low sampling frequency as about 20 kHz, and recovers a waveform to be measured. An up-to-date equivalent sampling oscilloscope can perform jitter measurement up to 40 Gbps in the time domain. Since it samples one by one in response to every trigger signal, however, the measurement time is too long and the time scale error is large. Moreover, the input channel of the equivalent sampling oscilloscope has a wideband, so it is too sensitive to the effect of noise, and therefore it cannot accurately measure small jitter.
The rapid progress in the high speed serial input/output technology requires a high speed measuring method, by which the wideband jitter of an oscillation can be measured at 5 Gbps or more without using a trigger signal and besides the measured value is hardly affected by the noise. However, such measuring method satisfying the requirement has not been invented yet. Meanwhile, even for the manufacturers of measuring devices, it is also difficult to develop high performance hardware (particularly, an analog-to-digital converter or a frequency counter) in order to realize the next generation real time oscilloscope or time interval analyzer. That is, the development of the next generation measuring devices is accompanied by considerable risk, because it requires long term development or significantly high development costs. In other words, it is obvious that the conventional measuring method has a limit. In this view, it is understandable that the invention of a frequency-scalable and simple measuring method without using a trigger signal is greatly significant.
The present invention proposes frequency domain sampling methods which can be used in the wideband jitter measurement. These sampling methods are frequency-scalable and considerably simple and can be widely applied even to a tester.
Next, the outline of the various conventional jitter measuring methods will be described. In order to distinguish them from the wideband jitter measuring method related to this invention, the conventional Δφ method will be referred to as a narrowband Δφ method. Tables 1 to 3 show the comparison of them with the proposed wideband jitter measuring method in the phase noise measurement, the dynamic jitter measurement, and the period jitter measurement respectively.
TABLE 1Comparison of measuring methods in thephase noise measurement.TIATIAOscillo.Oscillo.ZeroNon-ZeroΔφMethodSpectrumEquivalentΔφMethodReal TimeDead TimeDead TimeNarrowbandAnalyzerTimeWidebandMeasurementPossiblePossiblePossiblePossibleExcellentImpossibleExcellentPeakPossiblePossibleImpossiblePossibleImpossibleImpossiblePossibleJitterLowLowMediumHighAccuracyAccuracyAccuracyAccuracyfc1.5 GHz80 MHz2 GHz5 GHz50 GHz—40 GHzTmeasMediumShortExtremelyShortLong—Short toShortMediumJitter40 dB50 dB50 dB40 dB70 dB—50 dBDynamicor moreor moreRangeFrequencyDifficultDifficultDifficultDifficultFlexible—FlexibleScalabilityADC2D CounterNZD CounterADC———InternalTrigger————BPF—BPF+I, Q dem
TABLE 2Comparison of measuring methods in the dynamic jittermeasurement.TIATIAOscillo.Oscillo.ZeroNon-ZeroΔφMethodSpectrumEquivalentΔφMethodReal TimeDead TimeDead TimeNarrowbandAnalyzerTimeWidebandMeasurementPossiblePossiblePossiblePossibleImpossiblePossiblePossiblefc1.5 GHz80 MHz2 GHz5 GHz—40 MHz40 GHzTmeasMediumShortExtremelyShort—ExtremelyShort toShortLongMediumJitterSmallSmallMidiumSmall—LargeSmallFloorVariableEffectNoneNoneExistNone—ExistNoneOf TriggerInternalInternal/ExternalFrequencyDifficultDifficultDifficultDifficult—PossibleFlexibleScalabilityADC2D CounterNZD CounterADC—Trigger—InternalTrigger—Low SpeedBPFADC+I, Q dem
TABLE 3Comparison of measuring methods in the periodjitter measurement.TIATIAOscillo.Oscillo.ZeroNon-ZeroΔφMethodSpectrumEquivalentΔφMethodReal TimeDead TimeDead TimeNarrowbandAnalyzerTimeWidebandMeasurementPossiblePossiblePossiblePossibleImpossiblePseudoPossiblefc1.5 GHz80 MHz2 GHz5 GHz—40 MHz40 GHzTmeasMediumShortShortShort—ExtremelyShort toLongMediumJitterSmallSmallMediumSmall—LargeSmallFloorVariableEffectNoneNoneExistNone—ExistNoneOf TriggerInternalInternal/ExternalFrequencyDifficultDifficultDifficultDifficult—PossibleFlexibleScalabilityADC2D CounterNZD CounterADC—Trigger—InternalTrigger—Low SpeedBPFADC+I, Q dem
Next, the measurement method using a zero-crossing detector and the spectrum analyzer or the narrowband Δφ method in the time domain will be discussed.
From the Wiener-Khintchine theorem, the relations between an autocorrelation function Rxx(τ) and a two-sided autospectral density function Sxx(f) are given by
                                          R            xx                    ⁡                      (            τ            )                          =                  2          ⁢                                    ∫              0              ∞                        ⁢                                                            S                  xx                                ⁡                                  (                  f                  )                                            ⁢              cos              ⁢                                                          ⁢              2              ⁢              π              ⁢                                                          ⁢              f              ⁢                                                          ⁢              τ              ⁢                              ⅆ                f                                                                        (        1        )                                                      S            xx                    ⁡                      (            τ            )                          =                  2          ⁢                                    ∫              0              ∞                        ⁢                                                            R                  xx                                ⁡                                  (                  τ                  )                                            ⁢              cos              ⁢                                                          ⁢              2              ⁢              π              ⁢                                                          ⁢              f              ⁢                                                          ⁢              τ              ⁢                              ⅆ                τ                                                                        (        2        )            
The relations between Rxx(τ) and a one-sided autospectral density function Gxx(f) are given by
                                          R            xx                    ⁡                      (            τ            )                          =                              ∫            0            ∞                    ⁢                                                    G                xx                            ⁡                              (                f                )                                      ⁢            cos            ⁢                                                  ⁢            2            ⁢            π            ⁢                                                  ⁢            f            ⁢                                                  ⁢            τ            ⁢                          ⅆ              f                                                          (        3        )                                                      G            xx                    ⁡                      (            f            )                          =                  4          ⁢                                    ∫              0              ∞                        ⁢                                                            R                  xx                                ⁡                                  (                  τ                  )                                            ⁢              cos              ⁢                                                          ⁢              2              ⁢              π              ⁢                                                          ⁢              f              ⁢                                                          ⁢              τ              ⁢                                                ⅆ                  τ                                .                                                                        (        4        )            
An ideal oscillator outputs a repeated waveform represented byXIdeal(t)=cos(2πf0t+φ0).  (5.1)
However, an actual oscillator outputs an instantaneous value represented byx(t)=cos(2πf0t+φ0−Δφ(t)),  (5.2)
where Δφ(t) is a phase change, i.e. irregular deviation from a linear phase (2πf0t+φ0). Δφ(t) is called an instantaneous phase noise.
In consideration of an offset frequency fJ(=f−f0) from an oscillation frequency f0, the phase noise is regarded as the two-sided autospectral density function. From the equation (1), the autocorrelation function RΔφΔφ(τ) of the instantaneous phase noise is given by
                                                        R              ΔϕΔϕ                        ⁡                          (              τ              )                                =                      2            ⁢                                          ∫                0                ∞                            ⁢                                                                    S                    ΔϕΔϕ                                    ⁡                                      (                                          f                      J                                        )                                                  ⁢                cos                ⁢                                                                  ⁢                2                ⁢                π                ⁢                                                                  ⁢                                  f                  J                                ⁢                τ                ⁢                                  ⅆ                                      f                    J                                                                                      ,                            (        6        )            
where SΔφΔφ(fJ) is the two-sided phase noise autospectral density function. Using the one-sided phase noise autospectral density function GΔφΔφ(fJ) in equation (3), RΔφΔφ(τ) is given by 
                                          R            ΔϕΔϕ                    ⁡                      (            τ            )                          =                              ∫            0            ∞                    ⁢                                                    G                ΔϕΔϕ                            ⁡                              (                                  f                  J                                )                                      ⁢            cos            ⁢                                                  ⁢            2            ⁢            π            ⁢                                                  ⁢                          f              J                        ⁢            τ            ⁢                                          ⅆ                                  f                  J                                            .                                                          (        7        )            
Inversely, using the equation (2), the two-sided phase noise autospectral density function is given by
                                          S            ΔϕΔϕ                    ⁡                      (                          f              J                        )                          =                  2          ⁢                                    ∫              0              ∞                        ⁢                                                            R                  ΔϕΔϕ                                ⁡                                  (                  τ                  )                                            ⁢              cos              ⁢                                                          ⁢              2              ⁢              π              ⁢                                                          ⁢                              f                J                            ⁢              τ              ⁢                                                ⅆ                  τ                                .                                                                        (        8        )            
In the same way, using the equation (4), the one-sided phase noise autospectral density function is given by
                                          G            ΔϕΔϕ                    ⁡                      (                          f              J                        )                          =                  4          ⁢                                    ∫              0              ∞                        ⁢                                                            R                  ΔϕΔϕ                                ⁡                                  (                  τ                  )                                            ⁢              cos              ⁢                                                          ⁢              2              ⁢              π              ⁢                                                          ⁢                              f                J                            ⁢              τ              ⁢                                                ⅆ                  τ                                .                                                                        (        9        )            
If Δφ(t) is resampled near x(t)=0 or t=nT using a zero-crossing resampler, the timing jitter is represented byΔφ[n]=Δφ(t)|t=nT.  (10)
FIG. 1A shows the instantaneous timing jitter sequence Δφ[n]. The instantaneous period jitter sequence J[n] as shown in FIG. 1B is given by the differential of Δφ[n] asJ[n]=Δφ[n+1]−Δφ[n].  (11)
Using RΔφΔφ(τ) given by the equation (6) or (7), the jitter measurement is modeled in the time domain. The mean square value σ66 φ2 of the instantaneous phase noise Δφ(t) is given byσΔφ2=RΔφΔφ(0).  (12)
The autocorrelation coefficient RΔφΔφ(0) is the fluctuation power of a certain edge, and it should be noted that it is not the product of fluctuations of different edges.
The mean square value JRMS2 of the instantaneous period jitter sequence J[n] obtained by the equation (11) is given byJRMS2=2RΔφΔφ(0)−2RΔφΔφ(T).  (13.1)
In the same way,
                                                                                       J                RMS                2                                                                  m              ,              n                                2                =                                            R              ΔϕΔϕ                        ⁡                          (                              m                ,                m                            )                                -                                                    R                ΔϕΔϕ                            ⁡                              (                                  m                  ,                  n                                )                                      .                                              (        13.2        )            
Further, the mean square value JCC,RMS2 of an instantaneous cycle-to-cycle period jitter sequence JCC[n] is represented by
                                          J                          CC              ,              RMS                        2                    3                =                              2            ⁢                                          R                ΔϕΔϕ                            ⁡                              (                0                )                                              -                                    8              3                        ⁢                                          R                ΔϕΔϕ                            ⁡                              (                T                )                                              +                                    2              3                        ⁢                                                            R                  ΔϕΔϕ                                ⁡                                  (                                      2                    ⁢                    T                                    )                                            .                                                          (        14        )            
It should be noted that the autocorrelation coefficient RΔφΔφ(T) or RΔφΔφ(2T) does correspond to the product of the fluctuations of different edges. Therefore, in order to measure the period jitter or the cycle-to-cycle period jitter, it is necessary to observe the fluctuations of different edges at the same time.
From the equations (12) and (13.1), it is understood that RΔφΔφ(T) can be obtained by
                                          R            ΔϕΔϕ                    ⁡                      (            T            )                          =                              σ                          b              ⁢                                                          ⁢              ϕ                        2                    -                                                    J                RMS                2                            2                        .                                              (        15        )            
Using GΔφΔφ(fJ) given by the equation (9), the jitter measurement is modeled in the frequency domain. For τ=0 in the equation (7), σΔφ2 of the equation (12) is given by
                              σ                      Δ            ⁢                                                  ⁢            ϕ                    2                =                              ∫            0            ∞                    ⁢                                                    G                ΔϕΔϕ                            ⁡                              (                                  f                  J                                )                                      ⁢                                          ⅆ                                  f                  J                                            .                                                          (        16        )            
It should be noted that this is the Parseval's theorem. JRMS2 is obtained by
                              J          RMS          2                =                  4          ⁢                                    ∫              0              ∞                        ⁢                                                            G                  ΔϕΔϕ                                ⁡                                  (                                      f                    J                                    )                                            ⁢                                                sin                  2                                ⁡                                  (                                                            π                      ⁢                                                                                          ⁢                                              f                        J                                                                                    f                      0                                                        )                                            ⁢                                                ⅆ                                      f                    J                                                  .                                                                        (        17        )            
Further, JCC,RMS2 is represented by
                              J                      CC            ,            RMS                    2                =                  16          ⁢                                    ∫              0              ∞                        ⁢                                                            G                  ΔϕΔϕ                                ⁡                                  (                                      f                    J                                    )                                            ⁢                                                sin                  4                                ⁡                                  (                                                            π                      ⁢                                                                                          ⁢                                              f                        J                                                                                    f                      0                                                        )                                            ⁢                                                ⅆ                                      f                    J                                                  .                                                                        (        18        )            
Next, the jitter measurement in the time domain will be discussed. First, the fact that the time domain measurement is based on the zero-crossing time measurement will be shown. Then, the measurement principle of two types of time interval analyzers and two types of oscilloscopes will be described.
Since τ=0 in the equation (12), it is necessary to directly observe the fluctuation of a certain edge in order to measure o in the time domain. To directly observe the fluctuation of a certain edge of the oscillator under test, a perfect oscillator that provides a line shown in FIG. 2 is also required. That is, the instantaneous frequency of the output of the perfect oscillator does not depend upon time as shown by
                    1                  2          ⁢          π                    ⁢                        ∂          ϕ                          ∂          t                      =          f      0        ,where the inclination is stable as a constant line (i.e. without phase fluctuation). Practically, an oscillator of which phase noise is less than the test oscillator is used as the ideal oscillator (a reference oscillator in FIG. 3). In the conventional method as shown in FIG. 4, a time error function is measured as the time interval between the time of a rising edge of the output of the test oscillator and the time of a rising edge of the output of the ideal oscillator, and is given by
                                                        T              e                        ⁡                          (                              n                                  f                  0                                            )                                =                                    T              ⁡                              (                                  n                                      f                    0                                                  )                                      -                                          T                ref                            ⁡                              (                                  n                                      f                    0                                                  )                                                    ,                            (        19        )            
where the second term on the right-hand side in the equation (19) is the time of the rising edge of the output of the ideal oscillator. The time error function can be approximated by the timing jitter as
                                          -            2                    ⁢          π          ⁢                                          ⁢                      f            0                    ⁢                                    T              e                        ⁡                          (                              n                                  f                  0                                            )                                      =                              Δϕ            ⁡                          [              n              ]                                .                                    (        20        )            
Since a real time oscilloscope can continuously observe the edges of an oscillation waveform from the imperfect oscillator, the edges from the ideal oscillator may not be directly observed. That is, the edge times of the ideal oscillation output can be estimated by performing a least-square fit of a straight lines to the edges of the oscillation output measured. At this time, the effect of the frequency offset can also be minimized.
In the same way, since τ=0 and τ=T in the equation (13.1), it is understood in measuring JRMS2 that it is necessary to simultaneously observe the two edge fluctuations being apart from each other by T. In the conventional method, the period jitter is measured by directly measuring the time interval between two adjacent rising edges of a waveform to be measured and calculating its variance. Further, if the observation time interval τ is one period of the oscillation to be measured, the first increment of the time function or the time interval error is equivalent to the period jitter.
In summary, in order to measure the jitter in the time domain, it is necessary to measure the time interval between two different edges. That is, it is necessary to measure the time interval between the outputs of the oscillator under test and the ideal oscillator in case of the timing jitter measurement and the time interval between the adjacent rising edges of the outputs of the oscillator in case of the period jitter measurement. Accordingly, the zero-crossing method has been mainly used in the jitter measurement. Next, the zero-crossing detector-based measuring device in the prior art will be described.
The time interval analyzer of which dead time is zero continuously counts the sequence of zero-crossing times tk and the corresponding number of the zero-crossing k, using a zero-dead-time time-stamp counter. FIG. 5 shows the block diagram of the time interval analyzer of which dead time is zero.
For measuring the time interval, sampling rate should be only executed at the Nyquist sampling frequency. For example, the frequency range of the zero-dead-time time interval analyzer is limited to 80 MHz.
The second class of time interval analyzers count time intervals from a certain zero-crossing (referred to as a first zero-crossing) to n-th zero-crossing, using a counter of which dead time is non-zero.
Unlike the zero-dead-time time interval analyzer, the non-zero-dead-time time interval analyzer cannot directly measure the timing jitter.
Since it is necessary to sample the time interval at the Nyquist sampling frequency, the measurement limit of the time interval analyzer is about 4.5 Gbps. It takes only a short time in the period jitter measurement. For example, a probability density function of 10,000 points can be measured for about 60 msec or less. However, when the timing jitter occurring due to the periodic cause and the timing jitter occurring due to the random cause is separated or when the phase noise spectrum is measured, it is necessary to repeatedly measure the time interval and compute its autocorrelation function, and thus the measurement time becomes long. Moreover, since the measurement is basically performed one by one, the long-term timing jitter (long term jitter) or the cycle-to-cycle period jitter JCC[n] cannot be measured. In addition, to sample a high speed waveform, it is necessary to widen the bandwidth bw of the input cirucuit. Thus, when the wideband jitter is measured, the measurement is affected by the noise in proportion to √{square root over (bw)}.
The real time oscilloscope digitizes uniformity a waveform to be measured at a sampling period satisfying the sampling theorem (see FIG. 6). Further, the real time oscilloscope detects the zero-crossing point by performing interpolation on the discrete waveform and obtains the period jitter as the periodic change between the zero-crossing points.
In this method, there is a problem in principle (i.e. the problem of the measuring method associated with cyclostationary process) as described below. The 0% or 100% amplitude level portion of a jitter clock waveform corresponds to the stationary process. Meanwhile, the zero-crossing level is subject to the random phase modulation, so it corresponds to the non-stationary process. That is, the interpolation method in the real time oscilloscope is to perform interpolation on a portion of the waveform corresponding to the stationary process and estimate the zero-crossing time corresponding to the non-stationary process. From the portion of the waveform with causality, the edge without causality is estimated by force. If the jitter is large and the stationary process signal (which corresponds to the 0% or 100% amplitude level) is also affected by the jitter in the same way as the edge included in the non-stationary process, the jitter can be estimated relatively accurately in the interpolation method. However, if the jitter is small and the stationary process signal is not affected by the jitter, the jitter cannot be estimated accurately by the interpolation method.
It is obvious that the conversion speed of the analog-to-digital converter determines the upper limit of the measurement bandwidth in the method. For example, the jitter measurement can be performed up to 2.5 Gbps as shown in FIG. 7, using a real time oscilloscope of which sampling rate is 20 GSps. However, since the zero-crossing is hardly sampled, the most time-consuming portion of the method for estimating period jitter is in detecting the zero-crossing point. Further, since a high speed analog-to-digital converter (ADC) is realized by interleaving a plurality of sub-ADCs, the discrete waveform has a frequency component of interleaving operation or its harmonic components. Moreover, if the interleaved component occurs in a sideband of a carrier to be measured, the value of the jitter might be overestimated. Moreover, the measurement error of the period jitter is generally given by 1/(the mean square of the period jitter) of the waveform to be measured. Therefore, if the value of the jitter to be measured is small, the measurement error in this method becomes large. Moreover, in order to sample the high-speed waveform, it is necessary to widen the bandwidth bw of the input circuit. When the wideband jitter is measured, the measurement is affected by the noise in proportion to √{square root over (bw)}. Accordingly, the small jitter cannot be measured accurately. In addition, digitizing the waveform at accurate sampling timing requires making the sampling jitter small. Thus, the higher the data rate, the more the measurement is difficult.
An equivalent sampling oscilloscope increases its delay time, which is from a trigger point to a discrete point, and repeatedly digitizes the waveform using an ADC which is in operation at a low sampling frequency. Moreover, it reconstructs the original waveform so that it corresponds to the delay time with respect to the digitizing timing relative to the trigger timing (see FIG. 8).
If an equivalent sampling oscilloscope of which equivalent sampling rate is 40 MSps is used, the jitter measurement in the time domain can be possible up to 40 Gbps. However, the frequency domain measurement such as the phase noise spectrum measurement is impossible. Since the sampling period in the equivalent sampling method does not satisfy the sampling theorem, an aliasing error cannot be avoided at the frequency of 20 kHz or more. Moreover, 10,000 cycles of the input signal may occur between each sampled point during digitizing the input signal as shown in FIG. 9A, and plots them as if they are adjacent with each other when being plotted as shown in FIG. 9B. That is, the equivalent sampling oscilloscope cannot perform continuous measurement. Consequently, the period jitter cannot be measured in the equivalent sampling method. Inversely, since the time interval between the sampling values is not constant, the long term jitter cannot be measured neither in the equivalent sampling method. Further, since one sample is sampled in response to a trigger signal, the measurement time is too long. For example, it is reported that it takes about 15 seconds in the jitter measurement of 7600 bits. An oscilloscope has a measurement channel of 80 GHz for measuring the electric signal. Accordingly, the observation noise of the equivalent sampling oscilloscope itself is 3.5 times as large as the real time oscilloscope of 6 GHz. Therefore, it is difficult to realize the accuracy in the jitter measurement of a CMOS circuit of which noise energy is large.
A test apparatus system (an automatic test equipment system) using undersampling shown in FIG. 10 measures the timing jitter by undersampling a signal from a device under test. The signal from the device under test is probed by an HBS PROBE. The HBS PROBE supplies a START signal to a timing generator. The timing generator generates stop timing corresponding to the START signal and provides it as a trigger pulse to a comparator HBS PROBE. The HBS PROBE compares the signal level with a threshold level at the timing of the trigger pulse input as shown in FIG. 11 and outputs 0 if the signal is smaller than the threshold level or 1 if the signal is larger. As the test pattern is repeatedly applied to the device under test and the output signal is repeatedly undersampled, the edge transition of the signal can be obtained. A probability distribution function is obtained from the edge transition, and a probability density function is obtained by differentiating it.
A test apparatus using undersampling has a time scale error ΔφRMS(TimeScale) That is, it consists of the timing jitter ΔφRMS(TrigSig) of the START signal and the long term jitter σΔT(Delay) of the delay time which is from the time of the START signal to the stop timing. Accordingly, the frequency domain measurement such as the phase noise spectrum measurement is impossible. Further, since one sample is sampled in response to the START signal, the measurement time is too long. Therefore, it is difficult to apply this apparatus to the test of high-volume manufactured. It has been only applied to the evaluation of prototype devices. If the bandwidth bw of the signal path between the device under test and the comparator HBS PROBE is widened, the measurement is affected by the noise in proportion to √{square root over (bw)}. That is, the higher the test rate, the more the noise of the test system affects.
In the spectrum analyzer method or the phase detector method, to measure the phase noise in the frequency domain, the phase demodulated output Δφ(t) from a phase detector may be observed by using a spectrum analyzer as shown in FIG. 12.
However, in the spectrum analyzer method, since frequency is swept using a filter, it takes time in measurement. Moreover, since frequency sweep has to be performed on a filter, the frequency resolution is coarse. Accordingly, it is difficult to observe the spurious spectrum which occurs in the phase noise. Moreover, the spectrum analyzer method only measures the phase noise as the power spectrum. Therefore, the jitter transfer function can be estimated only by the ratio of the power spectrum of a phase noise to the power spectrum of another phase spectrum. Accordingly, in the spectrum analyzer method, the phase difference of the jitter transfer function cannot be measured. Moreover, in the spectrum analyzer method, the peak jitter of the phase noise cannot be measured. Further, the spectrum analyzer method cannot directly measure the rms value or the peak-to-peak value of the period jitter or its probability density function.
The narrowband Δφ method is to consider an instantaneous phase noise Δφ(t) as the phase modulation of the waveform and obtain a baseband signal Δφ(t) by demodulating the phase modulated signal.
In the narrowband Δφ method, the jitter is assumed to be phase modulated components which slowly change. In order to demodulate the phase modulated components, it is necessary to perform continuous sampling. Moreover, in the narrowband Δφ method, it is necessary to digitize the waveform to be measured more than 3 or 4 points per a period. That is, a high-speed ADC or a real time oscilloscope is required. Accordingly, although a real time oscilloscope of which sampling rate is 20 GSps is used, there is a limit that the jitter measurement is up to 5 GHz. Moreover, in order to sample a high-speed waveform, it is necessary to widen the bandwidth bw of the input system. When the wideband jitter is measured, the measurement is affected by the noise in proportion to √{square root over (bw)}. In addition, the faster the data-rate of the waveform-under-measurement, the more difficult it will be to digitize the waveform at accurate sampling timing without suffering from sampling jitter.